This was confirmed for \(1\le t\le 3\)  by Singer himself [1]} and Boardman [2]}. Our recent work [3]} shows that the conjecture is also true for \(t = 4.\) 
So far it remains open in general. Very little information is known when \(t = 5.\)  Now, based upon an admissible monomial basis for \(QP_5\)  in degree \(5(2^{s}-1) + 42.2^{s}\)  (see Theorem REF ), we verify Conjecture REF  for \(t = 5\)  and the respective degree. The following theorem is our second main result.
